Problem Setting: The goal in zero-shot domain generalization (ZSLDG) is to recognize unseen categories in unseen domains. Let \(Q^{Tr}=\lbrace  (\mathbf {x}, y, \mathbf {a}_y, d )| \mathbf {x} \in \mathcal {X}, y \in \mathcal {Y}^s, \mathbf {a}_y \in \mathcal {A}, d \in \mathcal {D}^s\rbrace \)  denote the training set, where \(\mathbf {x}\)  is a seen class image in the visual space (\(\mathcal {X}\) ) with corresponding label \(y\)  from a set of seen class labels \(\mathcal {Y}^s\) . Here, \(\mathbf {a}_y\)  denotes the class-specific semantic representation that encodes the inter-class relationships, while \(d\)  is the domain label from a set of seen domains \(\mathcal {D}^s\) . Note that the semantic representations are typically obtained from unsupervised text-based WordNet models (e.g, word2vec [1]})
Similarly, \(Q^{Ts}=\lbrace  (\mathbf {x}, y, \mathbf {a}_y, d )| \mathbf {x} \in \mathcal {X}, y \in \mathcal {Y}^u, \mathbf {a}_y \in \mathcal {A}, d \in \mathcal {D}^u\rbrace \)  is the test set, where \(\mathcal {Y}^u\)  is the set of labels for unseen classes and \(\mathcal {D}^u\)  represents the set of unseen domains. In the standard zero-shot setting, images at training and testing belong to disjoint classes but share the same domain space, i.e., \(\mathcal {Y}^s\cap \mathcal {Y}^u \equiv \emptyset \)  and \(\mathcal {D}^s\equiv \mathcal {D}^u\) . On the other hand, in the standard DG setting, images at training and testing belong to same categories in disjoint domain spaces, i.e., \(\mathcal {Y}^s\equiv \mathcal {Y}^u \)  and \(\mathcal {D}^s \cap \mathcal {D}^u \equiv \emptyset \) .
In this work, our goal is to address the more challenging ZSLDG setting for recognizing unseen classes in unseen domains without having seen these novel classes and domains during training, i.e., \(\mathcal {Y}^s\cap \mathcal {Y}^u \equiv \emptyset \)  and \(\mathcal {D}^s\cap \mathcal {D}^u \equiv \emptyset \) .
